The purpose of this project was to become an expert on a ride from Hershey Park. The ride chosen in the case of this assignment was Trailblazer.
The physics behind how the Trailblazer functions can be viewed throughout this page, as well as images of the ride itself and various graph. Enjoy the following.
Givens:
Some of the measurements that where used where not calculated at the park itself. There were materials available for reviewing, and thus these measurements where collected, and then used for other calculation throughout the site:
Length of train- 14.6 m
Height of first hill- 15.85 m
Time at the first hill- 20.86 sec
Average mass of a rider- 80.0 kg
Total mass of a loaded coaster- 3856 kg
Radius of the loop- 10.97 m
Velocity up the first hill- 2.5 m/s
Acceleration:
Graph #1: Horizontal Acceleration vs. Time to examine key parts of the ride
Here is a graph of the horizontal velocity of the ride, showing important parts of the ride. When looking at a graph of horizontal acceleration, one may notice the two areas of sporadic peaks in the graph. These areas show places where the ride went around horizontal loops. The peaks occur because the cart is undergoing rotational acceleration, and thus the horizontal (or tangential) acceleration is varying. Since the trailblazer has two parts with horizontal turns, there are two areas with these sporadic peaks.
Close-up of Graph #1
This is the close up of the graph, which shows the peaks and valleys where the ride underwent rotational acceleration
Graph #2: Vertical Acceleration vs. Time to examine key parts of the ride
When analyzing the acceleration graphs, it is important for one to look at the general trend of the lines rather than the specific points. Examination of the graphs shows many sporadic data points. One must make careful note that these points could be altered by the rigidness of the ride. Bumps in the ride could have caused the acceleration measurer to accelerate, thus taking data which is not consistent with the path of the track. While the graph does give a picture of the general movement of the roller coaster, it does not by any means get close to an exact representation of the cart.
Velocity:
Close up of Graph #2, to view the area under the curve
The graph was integrated in order to find velocity down the first hill. The area under an acceleration graph is the velocity, where as if the velocity were graphed then the area under that curve would be position. The velocity was found to be about 16 m/s.
Conservation of Energy:
The Law of Conservation of Energy is when the quantity being used is conserved. Sometimes the quantity may change, but the initial values equal the final values. In this case the quantity does not change but remains as energy, units being in Joules (J). The math that is seen below is the calculations of the potential and kinetic energies to see if the energy of the ride was conserved. The measurements taken were of the first hill in the ride.
The equation below is of the Law of conservation of energy.
KE (initial) + PE (initial) = KE (final) + PE (final) <- Since there is not any kinetic energy at the top of the hill, and no potential energy at the bottom of the hill, both the KE (initial) and PE (final) will be measured as zero, 0.
0 + mgy = 1/2mv^2 + 0 <- The mass can then be canceled out.
gy = 1/2v^2
(9.8 m/s^2)(15.85 m) = 1/2 (16 m/s)^2 <- The velocity was measure from finding the area under the curve of where the hill is located.
155.33 J = 128.00 J
The potential energy is greater than the kinetic energy, based on the calculations above. The missing energy was probably dispalced into friction, on the fact that the ride does not fall down but slowly eases down the track, thus the reason for the drop in energy.
Rotational Motion:
The coaster undergoes rotational motion because it goes through two horizontal loops at the end of the ride.
The angular acceleration can be found using the formula At= rα. At t=75s, when the cart was in the loop, the acceleration was .5m/s^2, which was found using the graphs seen above. The radius of the loop was given as 10.97m. The calculated angular acceleration value was .0456m/s^2. The velocity could be calculated using the formula v= 2πr/T. The period was found as 7.5s, using the graphs. At the park, the time the cart was in the loop was recorded. The velocity was found to be 9.19m/s. The centripetal acceleration was found using Ac= v^2/r. It was found to be 7.70 rad/s^2. The centripetal force was found using the formula F= mv^2/r. The average mass of a person is about 80kg. The force on a person was found to be 616 N.
Work:
Work is also done by the coaster. Work is defined as force along some distance traveled. Since the train is accelerating, force can be found and then applied along a specific distance.
The work done while the cart is in the loop can be done by using the above equation. The distance of the loop can be found using the equation C= 2πr. The length was 68.93m, and the work was found to be 42,454J.
Power:
Power can also be calculated for the coaster because it is work over a certain amount of time. Since the work was already calculated, power can be calculated during the loop using the equation P= W/t. The power for the coaster at this point was calculated to be 5,661W.
Newton's Law of Motion:
First law - “if the net force acting on the object is zero then the object will remain in the same motion. If resting it will stay resting, and if moving at a constant velocity it will stay at that constant velocity.” This could be used for very simple stuff on the Trailblazer. Before the ride starts and the people are just sitting in the train, the train stays stationary. This occurs because there is no force acting upon the train. Then when the chain grabs hold of the train to take it up the hill, it starts moving at a constant velocity. It stays at this constant velocity until the balance of forces are messed up by gravity by going down the hill. This law also applies for the end of the ride. When the ride is trying to stop the brakes are pumped and the people riding the train feel an almost whiplash affect, or in physics terms, inertia. This occurs because the train is moving at a constant velocity, and when the brakes are applied the train is deccelerating but the people in the train are still moving at the constant velocity. This happens because the people are not secure enough in the train and they don’t feel the brake effect until they hit the lab bar.
Second Law - “The acceleration is directly proportional to the force acting on it and inversely proportional to its mass.” So this gives us the equation F=ma. When applied to the Trailblazer there is a force as the train is pulled up the first hill. F = ma F = (3856 kg)(2.5 m/s) F = 9640 N
Possible Sources of Error:
The carts not being completely full and the average mass of the cart being different
Friction between the cart and the track
Human error
Analyzing the graph incorrectly because the ride was jumpy, causing the data to be jumpy
The Purpose:
The purpose of this project was to become an expert on a ride from Hershey Park. The ride chosen in the case of this assignment was Trailblazer.
The physics behind how the Trailblazer functions can be viewed throughout this page, as well as images of the ride itself and various graph. Enjoy the following.
Givens:
Some of the measurements that where used where not calculated at the park itself. There were materials available for reviewing, and thus these measurements where collected, and then used for other calculation throughout the site:Acceleration:
Graph #1: Horizontal Acceleration vs. Time to examine key parts of the ride
Here is a graph of the horizontal velocity of the ride, showing important parts of the ride. When looking at a graph of horizontal acceleration, one may notice the two areas of sporadic peaks in the graph. These areas show places where the ride went around horizontal loops. The peaks occur because the cart is undergoing rotational acceleration, and thus the horizontal (or tangential) acceleration is varying. Since the trailblazer has two parts with horizontal turns, there are two areas with these sporadic peaks.
This is the close up of the graph, which shows the peaks and valleys where the ride underwent rotational acceleration
Graph #2: Vertical Acceleration vs. Time to examine key parts of the ride
When analyzing the acceleration graphs, it is important for one to look at the general trend of the lines rather than the specific points. Examination of the graphs shows many sporadic data points. One must make careful note that these points could be altered by the rigidness of the ride. Bumps in the ride could have caused the acceleration measurer to accelerate, thus taking data which is not consistent with the path of the track. While the graph does give a picture of the general movement of the roller coaster, it does not by any means get close to an exact representation of the cart.
Velocity:
The graph was integrated in order to find velocity down the first hill. The area under an acceleration graph is the velocity, where as if the velocity were graphed then the area under that curve would be position. The velocity was found to be about 16 m/s.
Conservation of Energy:
The Law of Conservation of Energy is when the quantity being used is conserved. Sometimes the quantity may change, but the initial values equal the final values. In this case the quantity does not change but remains as energy, units being in Joules (J). The math that is seen below is the calculations of the potential and kinetic energies to see if the energy of the ride was conserved. The measurements taken were of the first hill in the ride.
The equation below is of the Law of conservation of energy.
KE (initial) + PE (initial) = KE (final) + PE (final) <- Since there is not any kinetic energy at the top of the hill, and no potential energy at the bottom of the hill, both the KE (initial) and PE (final) will be measured as zero, 0.
0 + mgy = 1/2mv^2 + 0 <- The mass can then be canceled out.
gy = 1/2v^2
(9.8 m/s^2)(15.85 m) = 1/2 (16 m/s)^2 <- The velocity was measure from finding the area under the curve of where the hill is located.
155.33 J = 128.00 J
The potential energy is greater than the kinetic energy, based on the calculations above. The missing energy was probably dispalced into friction, on the fact that the ride does not fall down but slowly eases down the track, thus the reason for the drop in energy.
Rotational Motion:
The coaster undergoes rotational motion because it goes through two horizontal loops at the end of the ride.The angular acceleration can be found using the formula At= rα. At t=75s, when the cart was in the loop, the acceleration was .5m/s^2, which was found using the graphs seen above. The radius of the loop was given as 10.97m. The calculated angular acceleration value was .0456m/s^2. The velocity could be calculated using the formula v= 2πr/T. The period was found as 7.5s, using the graphs. At the park, the time the cart was in the loop was recorded. The velocity was found to be 9.19m/s. The centripetal acceleration was found using Ac= v^2/r. It was found to be 7.70 rad/s^2. The centripetal force was found using the formula F= mv^2/r. The average mass of a person is about 80kg. The force on a person was found to be 616 N.
Work:
Work is also done by the coaster. Work is defined as force along some distance traveled. Since the train is accelerating, force can be found and then applied along a specific distance.The work done while the cart is in the loop can be done by using the above equation. The distance of the loop can be found using the equation C= 2πr. The length was 68.93m, and the work was found to be 42,454J.
Power:
Power can also be calculated for the coaster because it is work over a certain amount of time. Since the work was already calculated, power can be calculated during the loop using the equation P= W/t. The power for the coaster at this point was calculated to be 5,661W.Newton's Law of Motion:
First law - “if the net force acting on the object is zero then the object will remain in the same motion. If resting it will stay resting, and if moving at a constant velocity it will stay at that constant velocity.” This could be used for very simple stuff on the Trailblazer. Before the ride starts and the people are just sitting in the train, the train stays stationary. This occurs because there is no force acting upon the train. Then when the chain grabs hold of the train to take it up the hill, it starts moving at a constant velocity. It stays at this constant velocity until the balance of forces are messed up by gravity by going down the hill. This law also applies for the end of the ride. When the ride is trying to stop the brakes are pumped and the people riding the train feel an almost whiplash affect, or in physics terms, inertia. This occurs because the train is moving at a constant velocity, and when the brakes are applied the train is deccelerating but the people in the train are still moving at the constant velocity. This happens because the people are not secure enough in the train and they don’t feel the brake effect until they hit the lab bar.Second Law - “The acceleration is directly proportional to the force acting on it and inversely proportional to its mass.” So this gives us the equation F=ma. When applied to the Trailblazer there is a force as the train is pulled up the first hill.
F = ma
F = (3856 kg)(2.5 m/s)
F = 9640 N
Possible Sources of Error: